3. Extreme Earthquake Analysis

Earthquake prediction can be considered into two types. First is the statistical prediction which is based on previous events; Data are collected from the records. Second is deterministic prediction which is made from the earthquake signs. The table at Appendix shows the data for earthquakes in Gulf of Aqaba and surrounding area representing the minimum magnitude and maximum magnitude.

Most extreme event analysis is concerned with the distribution of annual maximum or minimum values at a given site. These events are given a rank, m, starting with m = 1 for the highest value, m = 2 for the next highest and so on in descending order. Each earthquake magnitude is associated with a rank, m, with m = 1 given to the maximum magnitude over the years of record, m = 2 given to the second highest magnitude, m = 3 given to the third highest one, etc. The smallest earthquake magnitude will receive a rank equal to the number of years over which there is a record, n. Thus, the discharge with the smallest value will have m = n = 18.

There are several formulas for calculating the probability value. The Weibull formula will be used because of its ease of use. The US Geological Survey [35] , among others, also uses this formula.

According to the Weibull equation [36] , the return period or recurrence interval T (in years) is calculated using the following equation:

(1)

where: m = event ranking (in a descending order), and n = number of events in the period of record.

The percentage probability the (annual exceedance probability) for each magnitude is calculated using the inverse of the Weibull equation as follows:

. (2)

From Equations ((1), (2)) it is clear that P = 100/T%. For example, an earthquake equal to that of a 10-year one would have an annual exceedance probability of 1/10 = 0.1 or 10%. This would say that in any given year, the probability that an earthquake with a magnitude equal to or greater than that of a 10-year earthquake would be 0.1 or 10%. Similarly, the probability of an earthquake with a magnitude exceeding the 50 year one in any given year would be 1/50 = 0.02, or 2%. Note that such probabilities are the same for every year, but in practice, such an earthquake could occur next year, or be exceeded several times in the next 50 years.

Table 1 shows the calculations of the rank m, the probability P and the return period T for the data of the yearly maximum magnitude given in the Appendix and Figure 5 shows the location of given data in the Appendix.

Figure 5. Location of give date in the Appendix [38] .

Table 1. The rank, probability and the return period results.

4. Earthquake Parameters

4.1. Annual Exceedance Probability and Return Period

Return period or Recurrence interval is the average interval of time within which a flood of specified magnitude is expected to be equaled or exceeded at least once. 19-year earthquake is an earthquake that is expected to occur, on the average, once every 19 years, or has 5.26% chance of occurring each year.

Figure 6 is a plot of earthquake magnitude and annual exceedance probability relationship (linear scales) with the annual maximum magnitude per year on the Y axis versus the annual exceedance probability on the X axis. The X and Y axes both use linear scales.

A best-fit curve is drawn through the data points. From the best-fit curve, one can determine the earthquake magnitude associated with an earthquake with a recurrence interval of say 1.9 years, it is about 3.95 on Richter scale. This would be called the 2-year earthquake.

Similarly, the recurrence interval associated with an earthquake magnitude of magnitude of 5.08 on Richter scale is about 19 years.

The annual peak information may also be presented with a logarithmic rather than a linear scale. This is often done to make the curve appear as a straight line and also to avoid a graph that will suggest either a zero or a one-hundred percent exceedance probability. Moreover, a straight line curves are more easily allow extrapolation beyond the data extremes. Figure 7 represents the earthquake magnitude and the annual exceedance probability (log scale) relationship.

Percentage probability is determined by dividing one by the recurrence interval and multiplying by 100. For example, the probability that an earthquake magnitude will exceed the 19-year earthquake this year or any other year would be 5.26%.

Figure 8 shows the earthquake magnitude and return period relationship on linear scales. From the figure it can be noticed that the return period of an earthquake of magnitude 5.08 on Richter scale is about 19 years, and an earthquake of magnitude of 4.44 on Richter scale has a recurrence interval of about 6.33 years.

Sometimes it is suitable to add a second Y-axis to represent the return period to the first Y-axis representing the annual exceedance probability. Figure 9 shows the earthquake magnitude on the X-axis and the annual

Figure 6. Earthquake magnitude and probability relationship (linear scales).

Figure 7. Earthquake magnitude and annual exceedance probability (log scale) relationship.

Figure 8. Earthquake magnitude and return period relationship (linear scales).

exceedance probability on the first Y-axis and the return period on the second Y-axis. Both the two Y-axes use avariable log scale so the relationship appears as a semi-parallel line, this will allow for easier findings.

From Figure 10, as the earthquake magnitude increased more than 3.3 on Richter scale the returned period will have increased and the probability will have decreased, this relation can be determined by the increment of the gap between the probability and return period lines.

Figure 9. Earthquake magnitude, probability and return period relationship.

Figure 10. Earthquake probability for some earthquake magnitudes in a time span period.

4.2. The Probability during a Time Period

Theprobabilityofacertain-magnitudeearthquakeoccurringduringanyperiod t can be calculated using the following equation:

(3)

where P is the probability of occurrence over the entire time period, t, and P is the probability of occurrence in any year.

It is worth to apply equation (3) for earthquakes of highest magnitudes which represent the most dangerous events in the study. The equation is applied for earthquakes of magnitudes 5.08, 4.65 and 4.44 Richter scale of probabilities of 5.26%, 10.52% and 15.78% respectively. The result is depicted in Figure 11 for earthquakes of magnitudes: 5.08 Richter scale (P = 5.26%), 4.65 Richter scale (P = 10.52%) and 4.44 Richter scale (P = 15.78%).

A homeowner considering the costs of reinforcing a house against earthquakes will want to know how the risk varies during an average mortgage span of 5 years. Figure 11 shows the earthquake probability and earthquake magnitudes in a time span of 5 years. An earthquake of magnitude of 4.44 on Richter scale for example, has a 57.65% probability of occurrence but, if the earthquake of magnitude 5.08 on Richter scale is chosen, the probability drops to 23.69%.

In addition, from Figure 11, any earthquake of magnitude less than 3.56 on Richter scale has a 100% probability of occurrence.

5. Conclusions and Points for Future Researches

5.1. Conclusions

Earthquake is an unavoidable natural disaster for the region. Hence, to take precautions for the future by utilizing the past experiences is very substantial. This can be a kind of a proposition to the higher authorities to have an open eye to this particular region.

In this study, the statistical frequency analyses are applied to the recorded annual maximum earthquake magnitudes for Gulf of Aqaba since 1999.

Figure 11. Earthquake probability and earthquake magnitudes in a time span of 5 years.

The earthquake hazard parameters are estimated, these are: the mean return periods (recurrence intervals), the frequency, the probability of earthquake occurrence (annual exceedance probability) for a given magnitude during any year, and the probability of earthquake occurrence for a given magnitude during a time span of t-years with a stress on a 18-year period. The Weibull equation is applied to estimate the return period, while the inverse of the Weibull equation is used to calculate the probability of occurrence.

The relation between magnitude and frequency and between magnitude and return period is represented as a curve in a linear scale graph and as a straight line on a logarithmic scale and variable scale graphs to facilitate the findings. The results lead to a general conclusion that Gulf of Aqaba is considered as a high seismic area and the region is exposed to earthquakes with strength ranging of 5 or more on the Richter scale with a high probability. The maximum magnitude is 5.08 with a return period of 19 years and probability of about 5.26%.

5.2. Points for Future Researches

Points for future researches can be summarized as follows:

・ To study in details the period before 1999 where it is included a recorded earthquake with magnitude 7.3 Richter scale on 1995.

・ To use other methods for evaluation of earthquake parameters and compare the obtained results.

・ To estimate earthquake hazard parameters for regions around Gulf of Aqaba.

・ To estimate hazard parameters for other events like: floods, subsidence, volcanic eruptions and severe storms in different regions around Gulf of Aqaba.

・ To draw a seismic map for Gulf of Aqaba region and for other regions around it.

Acknowledgements

We would like to present our appreciation to Professor Amar Ameen, Dean of the Faculty of Earth Sciences, King Abdulaziz University, Saudi Arabia and Assistant Professor Abdul-elah Bahabri, Engineering and Environmental Geology Department, King Abdulaziz University for their appreciated help.

In addition, special tanks to Hani Zahran, Directing Manager, National Center for earthquakes and volcanoes, Geological Survey Authority, Saudi Arabia, for providing all seismic reading of Gulf of Aqaba, which used in this paper.

Appendix

Data for the earthquakes in the Gulf of Aqaba from May, 1999 to Feb, 2016 [37] .

NOTES

^{*}Corresponding author.

Cite this paper

Baaqeel, A. , Quliti, S. , Daghreri, Y. , Hajlaa, S. and Yami, H. (2016) Estimating the Frequency, Magnitude and Recurrence of Extreme Earthquakes in Gulf of Aqaba, Northern Red Sea.*Open Journal of Earthquake Research*, **5**, 135-152. doi: 10.4236/ojer.2016.52011.

Baaqeel, A. , Quliti, S. , Daghreri, Y. , Hajlaa, S. and Yami, H. (2016) Estimating the Frequency, Magnitude and Recurrence of Extreme Earthquakes in Gulf of Aqaba, Northern Red Sea.

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